A discontinuous shapeless particle method for the quasi-linear transport

Abstract This paper considers a new version of the discontinuous particle method, whose higher accuracy is based on “predictor-corrector” scheme. The peculiarity this criterion rearranging particles at “corrector” stage. In contrast to previously used with analysis overlapping particles, which required an assumption about their form, we use another key characteristic namely, mass, more precisely, that in nonlinear elastic transport not only masses are conserved but also mass located between centers these particles. requirement leads fact changing distance process movement and conservation space them, lead change density one A arose solution two-dimensional problems. We emphasize discontinuity smeared into single particle, indicates high method. construction method for simple problem necessary step simulate complex gas dynamics